Microscopic wave functions of spin-singlet and nematic Mott states of spin-one bosons in high-dimensional bipartite lattices

We present microscopic wave functions of spin-singlet Mott insulating states and nematic Mott insulating states. We also investigate quantum phase transitions between the spin-singlet Mott phase and the nematic Mott phase in both large-N limit and small-N limit (N being the number of particles per site) in high-dimensional bipartite lattices. In the mean-field approximation employed in this article we find that phase transitions are generally weakly first order.